期刊
NATURE COMMUNICATIONS
卷 3, 期 -, 页码 -出版社
NATURE PORTFOLIO
DOI: 10.1038/ncomms1774
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资金
- National Science Foundation [DMR-0812204]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [0812204] Funding Source: National Science Foundation
Percolation on a one-dimensional lattice and fractals, such as the Sierpinski gasket, is typically considered to be trivial, because they percolate only at full bond density. By dressing up such lattices with small-world bonds, a novel percolation transition with explosive cluster growth can emerge at a non-trivial critical point. There, the usual order parameter, describing the probability of any node to be part of the largest cluster, jumps instantly to a finite value. Here we provide a simple example in the form of a small-world network consisting of a one-dimensional lattice which, when combined with a hierarchy of long-range bonds, reveals many features of this transition in a mathematically rigorous manner.
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